MaximalSecondExtensionOfSimplesWithRegularModule on DyckPath

The greatest dimension of the second extensions of a simple module by the regular module.

On DyckPath

FindStat's St001192.

Called as CombinatorialStat(x, "MaximalSecondExtensionOfSimplesWithRegularModule"). The head's page has its examples.

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Sizes 1 to

FindStat St001192

The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$.

Object	Value
[1,0]	0
[1,0,1,0]	1
[1,1,0,0]	0
[1,0,1,0,1,0]	1
[1,0,1,1,0,0]	1
[1,1,0,0,1,0]	1
[1,1,0,1,0,0]	2
[1,1,1,0,0,0]	0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001192 has the rest.